We can rule out genetics.
We can rule out upbringing.
We can rule out "choice".
What's left is fetal development - the process that builds a fetus from the genetic recipe - and a mutation in the progress of that development in one fetus.
I take issue with all three of your claims, and more generally reject the model under which you make them
Claim 1: Genetics.
Two issues emerge: firstly, there's the question of whether they're actually genetically identical - has this been tested? Or, as it usually the case, are they
assumed to be identical based on very similar morphology? It's not uncommon for twins to misclassified as identical. Even if they're monozygotic, it is quite possible for gene mutations to occur in one twin but not the other. Secondly, if we take a broader view of genetics, it's quite possible that the
epigenetics of the twins are different.
Claim 2: upbringing
Who says their upbringing was the same? Are we sure that, for example, the parents didn't pick up the differences in their play behaviour and encourage them, wanting to ensure their two sons developed different identities?
Claim 3: choice
Why can we rule out choice? Did Wyatt not choose tutus and beads? Did he not choose to demand a barbie cake? What is choice, anyway? The idea that it is only a choice if we could trivially choose differently is naive, at best.
Finally, I reject the framework underwhich you're working. Environment is wider than upbringing and the idea that the influences of genetics and environment can be separated is simply wrong. Many, probably most, genes - especially those for complex characteristics - interact with the environment is extremely varied ways. The influence of environment is
only possible if the genes allow it.
In a way,
all traits are 100% environmental and 100% genetic.